Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity

TL;DR

This paper constructs a dual two-dimensional theory for 3D asymptotically flat Einstein gravity at null infinity, revealing a connection to BMS3 invariant Liouville theory through Hamiltonian reduction.

Contribution

It develops a novel dual theory framework starting from Chern-Simons formulation, linking flat-space gravity to BMS3 invariant Liouville theory via gauge fixing and Hamiltonian reduction.

Findings

Derived a chiral WZW-like model based on Poincaré algebra

Performed Hamiltonian reduction to BMS3 invariant Liouville theory

Connected flat-space results to AdS case through gauge rephrasing

Abstract

Starting from the Chern-Simons formulation, the two-dimensional dual theory for three-dimensional asymptotically flat Einstein gravity at null infinity is constructed. Solving the constraints together with suitable gauge fixing conditions gives in a first stage a chiral Wess-Zumino-Witten like model based on the Poincar\'e algebra in three dimensions. The next stage involves a Hamiltonian reduction to a BMS3 invariant Liouville theory. These results are connected to those originally derived in the anti-de Sitter case by rephrasing the latter in a suitable gauge before taking their flat-space limit.